Question

For all sets A and B, A - $(A\cap B)$ is equal to ___

• A. $A^{\prime }\cap B$
• B. $A\cap B^{\prime }$
• C. $A^{\prime }\cap B^{\prime }$
• D. $(A\cup B{)}^{\prime }$

Answer 1

The correct option is B

$A\cap B^{\prime }$

$A-(A\cap B)=A\cap {(A\cap B)}^{\prime }=A\cap (A^{\prime }\cup B^{\prime })=(A\cap A^{\prime })\cup (A\cap B^{\prime })=\varphi \cup (A\cap B^{\prime })=A\cap B^{\prime }$